Finite Group DatabasebetaFinite Group Databasebeta| order | 9872 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C617 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #14578674 |
| commutator, hypocenter | C617 | C2×C8 |
| Frattini | C2 | C2×#14578674 |
| Fitting | C4×C617 | C4 |
| socle | C2×C617 | C2×C4 |
| prime radical | C2×D617 | C4 |
| cosocle | Dic617 | C22 |
| LCS | G ▷ C617 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,617|a^2=c,c^2=d,e^a=e^194,e^b=e^616,e^c=e^616632 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#14578674, #34089756, #34089764, … |
| maximal normal subgroup of | C8×#14578674, #34089756, #34089764, … |
| maximal quotient of | C4×#19096928, #34089759, #34089769, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9872, 48);